We still use Newtonian statics and dynamics in many situations even though we know they aren’t perfectly correct models.

I was a bit miff the other day when I read an article describing some experiment to measure a gravity effect never measured before, and the article summary was something like: "Experiment to test Newton's gravity". Surely that is incorrect.

It’s possibly a test for an obscure effect in Newtonian gravity (i.e. at low field strengths where the differences from General Relativity’s predictions are insignificant). Simple as it is, the inverse-square law of Newton has some intriguing mathematical properties that suggest odd measurable effects occurring in certain unusual configurations of masses and motions. Perhaps the best-known of these is that the n-body problem is inherently chaotic for n ≥ 3. However, I would need to see the article before I can make a more specific assessment.

Okay, it’s relatively straightforward. When the article speaks of “Newton’s gravity” it actually means gravity as described by General Relativity (GR). I suspect the writer chose the term “Newton’s gravity” because it’s an article targeted at a lay readership and very few non-specialists have a sufficient grasp of GR’s principles to appreciate what it says. Most people tend to think of gravity as a quasi-magical force that acts on something a bit like it were tied to the ground by billions of insubstantial but very stretchy rubber bands.

Newton himself was deeply troubled by gravity’s apparent action-at-a-distance because nobody was able to give a plausible explanation of how the force was mediated between gravitating bodies. That is, nobody had the faintest idea how gravity actually worked at the fundamental level. Nor did Newton’s gravitational law provide any clues. Einstein’s GR solved this long-standing puzzle. In essence, the presence of mass distorts (technically, “warps”) the spacetime around it and this warping affects how other bodies in its vicinity behave. Of course, those other bodies also warp the spacetime around themselves, similarly affecting yet other nearby bodies. The degree of spacetime warping depends principally on two factors, namely the mass of the body and the distance from its centre.

The underlying assumption in both Newton’s and Einstein’s models is that gravity is infinitely variable in its strength/range character, i.e. at a given range, gravity’s strength can vary continuously and any value is theoretically possible. The experiment described in the BBC article tests this assumption of perfect continuity. The results suggest that the assumption is wrong and that gravity is quantised in discrete (i.e. discontinuous) intensity packets. This is akin to electromagnetic effects that are mediated by photons whose energies can only come in certain distinct values. These phenomena seem to us continuous because of their submicroscopic granularity.

Perhaps a more familiar but less accurate analogy is the use of real (floating-point) numbers on a digital computer. The three standard floating-point types consist of 32, 64 or 80 bits. Since they consist of a finite number of bits, they can only represent a finite number of values, whereas the real numbers of arithmetic are uncountably infinite, meaning that there exist infinitely many non-equal real numbers between any two non-equal ones. There are thus infinitely many floating-point values that a digital computer cannot represent 100% accurately, and those numbers are disallowed in the “digital universe” (so to speak), just as certain photon energy values are disallowed in our universe.

(I quite enjoy explaining this stuff to an interested and intelligent audience, so no thanks are necessary.)

I suspect the writer chose the term “Newton’s gravity” because it’s an article targeted at a lay readership

....

The underlying assumption in both Newton’s and Einstein’s models is that gravity is infinitely variable in its strength/range character, i.e. at a given range, gravity’s strength can vary continuously and any value is theoretically possible. The experiment described in the BBC article tests this assumption of perfect continuity. The results suggest that the assumption is wrong and that gravity is quantised in discrete (i.e. discontinuous) intensity packets. -

Uhm, yeah, they failed spectacularly then. You just explained it much more succintly and understandably.